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logic

 
Dictionary: log·ic   (lŏj'ĭk) pronunciation
 
n.
  1. The study of the principles of reasoning, especially of the structure of propositions as distinguished from their content and of method and validity in deductive reasoning.
    1. A system of reasoning: Aristotle's logic.
    2. A mode of reasoning: By that logic, we should sell the company tomorrow.
    3. The formal, guiding principles of a discipline, school, or science.
  2. Valid reasoning: Your paper lacks the logic to prove your thesis.
  3. The relationship between elements and between an element and the whole in a set of objects, individuals, principles, or events: There's a certain logic to the motion of rush-hour traffic.
  4. Computer Science.
    1. The nonarithmetic operations performed by a computer, such as sorting, comparing, and matching, that involve yes-no decisions.
    2. Computer circuitry.
    3. Graphic representation of computer circuitry.

[Middle English, from Old French logique, from Latin logica, from Greek logikē (tekhnē), (art) of reasoning, logic, feminine of logikos, of reasoning, from logos, reason.]


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The sequence of operations performed by hardware or software. It is the computer's "intelligence." Hardware logic is contained in the electronic circuits and follows the rules of Boolean logic. Software logic (program logic) is contained in the placement of instructions written by the programmer. Software logic is called "business logic" when it refers to the transactions of the business rather than underlying infrastructure such as the operating system, database management system (DBMS) or network.

Logic Is Not Logical

The term "logic" is not the same as "logical." Logic refers to algorithms and operational sequences; whereas, "logical" refers to a higher-level view of hardware, software or data that is not tied to physical structures (see logical vs. physical). See also logical expression.

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Thesaurus: logic
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noun

  1. Exact, valid, and rational reasoning: ratiocination, rationality, reason. See reason/unreason.
  2. What is sound or reasonable: rationale, rationality, rationalness, reason, sense. Idioms: rhyme or reason. See reason/unreason.

 
Antonyms: logic
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n

Definition: science of reasoning
Antonyms: unreasonableness


 
Dental Dictionary: logic
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n

A disciplined method of reasoning or argumentation that employs the principles governing correct or reliable inference.

 

Study of inference and argument. Inferences are rule-governed steps from one or more propositions, known as premises, to another proposition, called the conclusion. A deductive inference is one that is intended to be valid, where a valid inference is one in which the conclusion must be true if the premises are true (see deduction; validity). All other inferences are called inductive (see induction). In a narrow sense, logic is the study of deductive inferences. In a still narrower sense, it is the study of inferences that depend on concepts that are expressed by the "logical constants," including: (1) propositional connectives such as "not," (symbolized as ¬), "and" (symbolized as Ù), "or" (symbolized as Ú), and "if-then" (symbolized as É), (2) the existential and universal quantifiers, "($x)" and "(x)," often rendered in English as "There is an x such that …" and "For any (all) x, …," respectively, (3) the concept of identity (expressed by "="), and (4) some notion of predication. The study of the logical constants in (1) alone is known as the propositional calculus; the study of (1) through (4) is called first-order predicate calculus with identity. The logical form of a proposition is the entity obtained by replacing all nonlogical concepts in the proposition by variables. The study of the relations between such uninterpreted formulas is called formal logic. See also deontic logic; modal logic.

For more information on logic, visit Britannica.com.

 

The general science of inference. Deductive logic, in which a conclusion follows from a set of premises, is distinguished from inductive logic, which studies the way in which premises may support a conclusion without entailing it. In deductive logic the conclusion cannot be false if the premises are true. The aim of a logic is to make explicit the rules by which inferences may be drawn, rather than to study the actual reasoning processes that people use, which may or may not conform to those rules. In the case of deductive logic, if we ask why we need to obey the rules, the most general form of answer is that if we do not we contradict ourselves (or, strictly speaking, we stand ready to contradict ourselves. Someone failing to draw a conclusion that follows from a set of premises need not be contradicting him or herself, but only failing to notice something. However, he or she is not defended against adding the contradictory conclusion to his or her set of beliefs.) There is no equally simple answer in the case of inductive logic, which is in general a less robust subject, but the aim will be to find reasoning such that anyone failing to conform to it will have improbable beliefs. Aristotle is generally recognized as the first great logician, and Aristotelian logic or traditional logic (see syllogism) dominated the subject until the 19th century. It has become increasingly recognized in the 20th century that fine work was done within that tradition, but syllogistic reasoning is now generally regarded as a limited special case of the forms of reasoning that can be represented within the propositional and predicate calculus. These form the heart of modern logic. Their central notions, of quantifiers, variables, and functions were the creation of the German mathematician Frege, who is recognized as the father of modern logic, although his treatment of a logical system as an abstract mathematical structure, or algebra, had been heralded by Boole (see Boolean algebra). Modern logic is thus called mathematical logic for two reasons: first, the logic itself is an object of mathematical study, but secondly, the forms introduced by Frege provided a language capable of representing all mathematical reasoning. This was something traditional logic had been quite incapable of tackling. The propositional and predicate calculus study ways of combining propositions with the connectives expressing truth-functions, and of combining information about the quantity of times predicates are satisfied. These highly general operations can occur in any discourse, from mathematics to discussion of the football results. More specific logics study particular topics such as time, possibility, and obligation. Thus there exist deontic logics, modal logics, logics of tense, and so on. For other notions associated with the study of logic see interpretation, logical calculus, logical constants, logical form, model theory, proof theory, quantifier, truth-function, variable.

 
logic, the systematic study of valid inference. A distinction is drawn between logical validity and truth. Validity merely refers to formal properties of the process of inference. Thus, a conclusion whose value is true may be drawn from an invalid argument, and one whose value is false, from a valid sequence. For example, the argument All professors are brilliant; Smith is a professor, therefore, Smith is brilliant is a valid inference, but the argument All professors are brilliant; Smith is brilliant; therefore, Smith is a professor is an invalid inference, even if Smith is a professor.

Aristotelian Logic

In Western thought, systematic logic is considered to have begun with Aristotle's collection of treatises, the Organon [tool]. Aristotle introduced the use of variables: While his contemporaries illustrated principles by the use of examples, Aristotle generalized, as in: All x are y; all y are z; therefore, all x are z. Aristotle posited three laws as basic to all valid thought: the law of identity, A is A; the law of contradiction, A cannot be both A and not A; and the law of the excluded middle, A must be either A or not A.

Aristotle believed that any logical argument could be reduced to a standard form, known as a syllogism. A syllogism is a sequence of three propositions: two premises and the conclusion. By varying the form of the proposition and the modifiers (such as all, no, and some), a few specific forms may be delimited. Although Aristotle was concerned with problems in modal logic and other minor branches, it is usually agreed that his major contribution in the field of logic was his elaboration of syllogistic logic; indeed, the Aristotelian statement of logic held sway in the Western world for 2,000 years. Nonetheless, various logicians did, during that time, take issue with parts of Aristotle's thought.

Post-Aristotelian Logic

One of Aristotle's tacit assumptions was that there is a correspondence linking the structures of reality, the mind, and language (and hence logic). This position came to be known in the Middle Ages as realism. The opposing school of thought, nominalism, is exemplified by William of Occam, a medieval logician, who maintained that the structure of language and logic corresponds only to the structure of the mind, not to that of reality. Since knowledge is a study of generalizations, while nature occurs in myriad single instances, the distinction between the world and our conception of it is stressed by the nominalists.

Inductive Reasoning

In the 19th cent. John Stuart Mill noticed the same dichotomy between man's generalizations and nature's instances, but moved toward a different conclusion. Mill held that the scientist or experimenter is not interested in moving from the general to the specific case, which characterizes deductive logic, but is concerned with inductive reasoning, moving from the specific to the general (see induction). For example, the statement The sun will rise tomorrow is not the result of a particular deductive process, but is based on a psychological calculation of general probability based on many specific past experiences. Mill's chief contribution to logic rests on his efforts to formulate rules of inductive logic. Although since the criticisms of David Hume there has been disagreement about the validity of induction, modern logicians have argued that inductive logic does not need justification any more than deductive logic does. The real problem is to establish rules of induction, just as Aristotle established rules of deduction.

Mathematics and Logic

With the development of symbolic logic by George Boole and Augustus De Morgan in the 19th cent., logic has been studied in more purely mathematical terms, and mathematical symbols have replaced ordinary language. Reference to external interpretations of the symbols (formulated in ordinary language) was also rejected by the formalist movement of the early 20th cent. Bertrand Russell and Alfred North Whitehead, in Principia Mathematica (3 vol., 1910–13), attempted to develop logical theory as the basis for mathematics. Pure formal logic attempts to prove that a logical system is dependent only on the perceptual recognition and valid manipulation of symbols and requires no interpretive reference to content.

Intuitionism, rejecting such formalism, holds that words and formulas have significance only as a reflection of activity in the mind. Thus a theorem has meaning only if it represents a mental construction of a mathematical or logical entity. Kurt Gödel, in the 1930s, brought forth his “incompleteness theorem,” which demonstrates that an infinitude of propositions that are underivable from the axioms of a system nevertheless have the value of true within the system. Neither these Gödel Propositions, as they are called, nor their negations are provable. One implication for the modern logician is that Aristotle's law of the excluded middle (either A or not A) is neither so simple nor so self-evident as it once seemed.


 
History 1450-1789: Logic
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Recent research on the seemingly staid subject of logic has revealed not only that certain topics in logic explained how inductive reasoning came about, but also that logic itself learned to create its own history in which logic arose from simple beginnings, but over time developed ever better ways of thinking, eventually becoming a progressive force in the history of thought. Furthermore, by the eighteenth century, the history of logic served as the structure for the history of philosophy, as well as an encyclopedia of knowledge known as historia literaria.

Although the importance of inductive reasoning to natural philosophy has been acknowledged, other research has shown that the tradition of inductive logic, which historians of the scientific revolution have identified as new, was actually developed by Aristotelian philosophers. The best known of these is the Paduan philosopher Jacobo Zabarella. His logic developed in part as a criticism of Florentine Neoplatonism and the medieval Scotist philosophy. This tradition of logic was taught not only in Italy but also in England, where logic texts by Zabarella have been found to have been used as school texts. Further, in Germany there remain today ninety-seven copies of Zabarella's Opera Logicae. This logic was then adopted by Bartholomew Keckerman for more elementary teaching and finally adopted again during the second half of the seventeenth century in Finland and Scandinavia after the Ramus vogue had run its course. Finally, at Jena, texts by Zabarella and the Coimbra commentators from Portugal were seen to be the beginning of a tradition of logic that led to the philosophy of John Locke (1632–1704) and Robert Boyle (1627–1691).

The best way to explain the difference between the Neoplatonic and Scotist approaches to knowledge and logic is to follow the debate around what is now considered a guiding logical and philosophical question between 1500 and 1750: What was the first thing thought? Was it the pure concept of an object or idea as defined by the Neoplatonists and some Scotists, that is, an idea conceived in the mind without recourse to the unreliable senses? Was it being, or ens, as Thomas Aquinas wrote? Or was it a fuzzy notion of a whole object or concept that needed to be examined, carefully defined and refined, and finally, when more was known about it, completely reexamined?

The great innovators of logic in the seventeenth century—Francis Bacon (1561–1626), Pierre Gassendi (1592–1655), Robert Boyle, and John Locke—continued and transformed this anti-Platonic, anti-Scotist tradition. These anti-Platonic philosophers held that there were two types of knowledge, divine and human, each with its own method. Divine knowledge was accessed through inspiration; human knowledge, or artificial knowledge, had to be learned through the senses. The anti-Platonists often quoted Aristotle as saying, "There is nothing in the mind that is not in the senses."

Many philosophers did work on inductive reasoning, beginning with the sixteenth-century Aristotelians Benedito Pereira in Rome and Zabarella in Padua. Their work was drawn upon and transformed by Bacon, Boyle, and Locke in England, Gassendi and his followers in France, and members of a new German school of philosophy known as eclecticism. The eclectics, like their counterparts in England and France, were both anti-Platonic and anti-Cartesian. They gave their tradition a historical dimension, writing that since no human being could know everything, philosophers should examine the reasoning of past philosophers, criticize or accept the methods they had used to reach their conclusions, and finally judge the validity of the original concepts. Using improved logic, each philosopher would then add new information to explain his findings. Eclecticism also referred to a Neoplatonic philosophy that tried to unify all knowledge under one idea by such early church fathers as Clement of Alexandria. Although it had the same name, this was very different from German eclecticism.

How is it possible to classify Gassendi, Bacon, and Locke together? Here one can realize the pitfalls of assigning one name to logical schools. For example, Gassendi did write a treatise attacking scholastic logic, Adversus Aristoteleos as he called it. This treatise was really attacking the self-referential syllogistic reasoning of dialectic, and often criticizes the Scotist philosopher Eustachius St. Paul, teacher of Descartes, and quotes Benedito Pereira, the anti-Platonic and anti-Scotist Aristotelian at the Collegio Romano. Gassendi dismissed Eustachius as Scholastic or Aristotelian, while he was developing his own version of the anti-Platonic logic of the sixteenth century that he reworked with his own recreation of Epicurean logic.

A further discussion of logic can be reduced to five points: 1) the use of rhetoric as a tool of persuasion by logicians; 2) the transformation of logic by anti-Platonic Aristotelian philosophers and their development of the question, De primo cognito?, 'What was the first thing thought?'; 3) this orientation of logic leads to the very specific criticism of the Neoplatonic myth of the prisca philosophiae, the 'first philosophers'; 4) the development of a technical vocabulary for natural philosophy that was a direct result of inductive logic: as myth and metaphor were rejected for biblical commentary, so Platonic myth and metaphor was to be shunned for inductive reasoning; 5) the hermeneutic of language for logic, which was then applied to the writings of logicians in the past and provided a tool for judging past thought. Thus the history of philosophy was born, and its midwife was logic.

Rhetoric and Logical Reasoning

The scholarship of Letizia Panizza and Heikki Micheli has made it quite clear that, as Micheli writes, "there is no justification for separating rhetoric from logic." The model of the correct logical proof changed dramatically when techniques of rhetoric were used. As Panizza explains, medieval philosophers "who learned their dialectic mainly from Boethius commentaries on Cicero and manuals of logic did not pay attention to Aristotle and Cicero on the close rapport of dialectic and rhetoric" (Cicero's De Oratore, a work only known after 1421). Panizza also explains that by the end of the fifteenth century, "Aristotle is held up as a model for an orator who wants to unite not only eloquence with philosophy in general, but rhetoric with dialectic."

She goes on to explain that logic was the instrument for philosophical thought, while rhetoric was the technique used to convince the reader. The philosophers adopted the persona of the orator, which was about the only technique used by Renaissance historians. By the time Zabarella (1532–1589) published De Methodis in 1578, rhetoric was being used to convince the reader of his method. Zabarella began each book of his treatises with a summary statement of method in which he declared his objectivity about his topic and his modesty towards knowledge, just as historians before him had done. After declaring his objectivity, he stated why his method of logic was superior to all others.

But the philosopher's use of the first person, in imitation of the speech of an orator, really developed in France with René Descartes's (1596–1650) Discourse on Method and Gassendi's persuasive voice in the Syntagma. In his work, Descartes declared the originality of his thoughts. He tended to assert the truth of his logical statements with rhetorically styled sincerity rather than engage in argument. Regius, a fellow philosopher, was so annoyed at the Cartesian use of persuasion rather than logic for proof that he wrote to Descartes, "any mad man can claim he is right." Descartes declared, "I think therefore I am." On the contrary, the first thing thought by Gassendi was not an a priori judgment; to him, thought had a history. He studied what past philosophers had thought, and he judged and critically examined the logic of the position. This led him to write a history of logic, the first comprehensive history up to that time.

Anti-Platonic Philosophers

Charles Schmitt wrote that Zabarella's logic set the stage for the logic used in the seventeenth century. Logic texts quoted Zabarella's attack on a priori reasoning and praised his logical method of setting out information not only in the seventeenth century but into the eighteenth. Johann Syrbius of Jena began his 1715 logic text with a critical history of the attack against a priori reasoning. He begins with a short historical discourse on the proposition that species originated in the mind, beginning with a quote from a commentary on Aristotle's De anima by the Portuguese Coimbra philosopher and Zabarella and ending by having linked the earlier traditions with the contemporary philosophy of John Locke and Robert Boyle. He also criticized Descartes, who believed that the species originated in the mind.

Neoplatonism

Not only was a priori reasoning rejected by specific philosophers, but the same anti-Platonic argument was used against the nonhistorical view that the prisci philosophiae or prisci sapientes could have known all of human knowledge without having learned it. For the Neoplatonists there was one truth that could be found in different forms in different religions around the world. This universal truth was proposed in the fifteenth century by Marsilio Ficino and was still of interest in the seventeenth to the Jesuit polymath Athanasius Kircher. Kircher's magnificently illustrated book of Noah's Ark, in which all of the knowledge known intuitively by early man is set out among the rooms, is a delightful visualization of universal knowledge.

There was an encyclopedia based on the other view. Zabarella said that as unlearned men, the prisci only knew what was in their nature. As the first thing thought was only hazily understood and had to be observed, identified, and then named, human civilization followed the same pattern. Initially humans knew nothing and had to understand the world through trial and error. A clever person appeared and made improvements, then others asked to become apprentices so that they could learn the logic of that person's way of working. Finally, all of this knowledge was written down. Adam, Moses, and Hermes Trimegistus are not part of this world: they all had only natural knowledge.

Just as there was not only one universal truth, there was not only one logical method for all disciplines. The greatest and most comprehensive history of disciplines was set out in 1708 in the Polyhistor by Georg Morhof (1639–1691). He articulated the difference between the disciplines as a logician articulates the difference between different sense impressions in inductive reasoning. Once the field of learning was identified, then the early and unclear beginnings of thought could be described and its history told as the history of the progress of the logic of that field of knowledge.

The Vocabulary of Natural Philosophy

If logic could control the organization of knowledge, it also dictated correct vocabulary. Research has shown that this hermeneutics of language was used as a weapon against Platonic philosophers. Perhaps no one was criticized for his vocabulary more than Paracelsus (c. 1493–1541), the innovative medical philosopher who developed a vocabulary for spells to use in medicinal cures. Medical doctors like the Swiss Thomas Erastus (1524–1583) attacked the Paracelsian language of spells for its attempt to be universal. Erastus said that no word is universal, but is particular to the civilization in which it is found. Spells and magic tried to unite heaven and earth into a chain of being that did not exist, Erastus complained. He asserted that there was a separation between the realms.

If natural philosophy and medical science were to improve, logic had to be used. Logic must order sense perceptions in such a way that what is known is recorded and what is unknown discovered. To do this, a precise vocabulary had to be devised. There was such interest in identifying the correct type of vocabulary for inductive reasoning and identifying Platonic or Scotist definitions that at the turn of the seventeenth century Goclenius's Lexicon was published, which set out the different types of words for different types of logic.

Application of Logic to the Philosophy of the Past

Not long after Zabarella's attack on the logic of prisci sapientes, the various types of logic of the various philosophers came under scrutiny. Anthony Grafton pointed out that Isaac Casaubon discovered that the Neoplatonic texts by Hermes Trismegistus were third-century forgeries. This discovery paved the way for a reassessment of Egyptian civilization. When the logic of earlier philosophers was identified, examined, and judged, an important change occurred: the critical characterization of the logic of past philosophers, the identification of philosophers not chronologically but by the success of their logic, changed the way people viewed past philosophy.

Pierre Gassendi wrote the first history of logic. His little-known work De Logicae Origine et Varietate, published in 1648 as a preface to the Syntagma, took the reader on an intellectual trip from the logic of Adam to the logic of Descartes. Adam, wrote Gassendi, did not have logic when he argued with the snake: "He was merely quibbling." He also argued that none of the patriarchs in the Bible were capable of logic either. Logic began with the Greeks and Zeno. Gassendi then criticized Plato's logic because it depended on a priori thinking and "was too much like theology." Although he admitted there was much to admire in Aristotle's logic, Gassendi wrote that it had been spoiled by his followers.

Gassendi admired the logic of the ancient philosopher Epicurus, based on inductive reasoning. Gassendi constructed a believable Epicurean logic in this text that appeared in student logic texts until the mid-eighteenth century. Jean le Clerc, friend of both Robert Boyle and John Locke, wrote perhaps the most widely used of these logic texts. From Epicurus, Gassendi passed over the Middle Ages, cramming one thousand years into two paragraphs, then began in the early modern period with Francis Bacon and the establishment of inductive reasoning. Bacon, wrote Gassendi, went the "heroic way." Gassendi made Bacon as the hero of contemporary thought. There is a great deal of rhetoric in this history of logic.

Finally, the complete triumph of logic as the history of logic came with the work of the German historian of philosophy Jacob Brucker (1696–1770). At Jena, Brucker was a student of Johan Jacob Syrbius, who had linked contemporary English inductive reasoning with the earlier logic of the Coimbra commentaries and Zabarella's De Methodis. In 1723, Brucker wrote a history of logic called Historia Philosophia Doctrinae de Ideis. In this work he attacked the prisca philosophiae in the person of Zoroaster. Following Gassendi, whose history of logic he knew, Brucker judged each philosopher by whether he used inductive reasoning. He praised Epicurus among the ancient philosophers and dismissed Renaissance philosophers like Valla and Vives, while praising John Locke and Robert Boyle.

Although the early modern period saw many breaks with past tradition, it did not usher in a new logic all at once. Rather, it was a period in conversation with past philosophy: sometimes it agreed, sometimes it disagreed, and sometimes the philosopher transformed his sources beyond recognition. As the De primo cognito? question was reworked by the anti-Platonic philosophers, the concept of intellectual (as opposed to chronological) progress developed in the sixteenth and seventeenth centuries. Nowhere can the concept of progress be seen more clearly than in the history of logic.

Bibliography

Primary Sources

Brucker, Jacob. Historia Philosophia Doctrinae de Ideis. Augsburg, 1723.

——. "De Reformatione Philosophiae Rationalis Recentiori Aetate Tentata." In Historia Critica Philosophiae. 2nd ed. Leipzig, 1754. Reprint with English translations of Brucker's Praefatio and definitions of Eclecticism and Syncretism, edited by Constance Blackwell. Bristol. Forthcoming.

Gassendi, Pierre. "De Logicae Origine et Varietate." In Opera Omnia, vol. 1, pp. 35–66. Leiden, 1658. Reprint, Stuttgart-Bad, 1994. The English translation, Pierre Gassendi's "Instutio Logica" (1658): A Critical Edition and Introduction by Howard Jones (Assen, 1981) does not include a translation of Gassendi's history of logic.

Syrbius, J. J. Institutiones Philosophiae Primae Novae et Eclecticae. Jena, 1720.

——. Institutiones Philosophiae Rationalis Eclectica, in Praefatione Historia Logicae Succincte Delineatur. Jena, 1717.

Toletus, Francescus. Commentaria Una cum Questionibus in Octo Libros Aristotelis de Physica Auscultatione. First edition, Cologne, 1574; last edition, Venice, 1615. Reprint, Hildesheim, 1985.

——. Commentaria Una cum Questionibus in Universam Aristotelis Logicam. First edition, Rome, 1572; last edition, Cologne 1615. Reprint, Hildesheim, 1985.

Zabarella, Jacobo. Opera Logica. Frankfurt, 1608 and 1966.

Secondary Sources

Blackwell, Constance. "Epicurus and Boyle, Le Clerc and Locke: Ideas and Their Redefinition in Jacob Brucker's Historia Philosophica Doctrinae de Ideis 1723." In Il vocabolario della République des Lettres: Terminologia filosofica e storia della filosofia, problemi di metodo, in memoriam di Paul Dibon, edited by Marta Fattori. Naples, 1997.

——. "The Logic of the History of Philosophy: Morhof's 'De Variis Methodis' and the Polyhistor Philosophicus." In Mapping the World of Learning: The Polyhistor of Daniel Georg Morhof, edited by Françoise Waquet, pp. 35–50. Wiesbaden, 2000.

——. "Vocabulary as a Critique of Knowledge: Zabarella and Keckermann—Erastus and Conring." In Philologie und Erkenntnis: Beiträge zu Begriff und Problem Frühneuzeitlicher "Philologie," edited by Ralph Häfner. Tübingen, 2002.

Mikkeli, Heiki. An Aristotelian Response to Renaissance Humanism: Jacopo Zabarella on the Nature of the Arts and Sciences. Helsinki, 1992.

Panizza, Letizia. "Ermolao Barbaro e Pico della Mirandola tra retorica e dialettica." De genere dicendi philosophorum del 1484, Ermolao Barbaro (1454–1493) Congress, edited by Michela Marangoni. Venice, 1996.

—CONSTANCE BLACKWELL

 

The principles of reasoning.

 

Science of dealing with the principle and applications of gates, relays and switches.


 
A cynical view of the world by Ambrose Bierce


n.

The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion -- thus:

Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.

Minor Premise: One man can dig a posthole in sixty seconds; therefore --

Conclusion: Sixty men can dig a posthole in one second.

This may be called the syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.



 
Word Tutor: logic
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pronunciation

IN BRIEF: The science of correct thinking or sound reasoning.

pronunciation Better to be without logic than without feeling. — Charlotte Bronte (1816-1855)

 
Quotes About: Logic
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Quotes:

"Logic is like the sword -- those who appeal to it, shall perish by it." - Samuel Butler

"Logic is a poor guide compared with custom." - Winston Churchill

"The mind has its own logic but does not often let others in on it." - Bernard Devoto

"Man is not logical and his intellectual history is a record of mental reserves and compromises. He hangs on to what he can in his old beliefs even when he is compelled to surrender their logical basis." - John Dewey

"From a drop of water a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other." - Sir Arthur Conan Doyle

"Logic, like whiskey, loses its beneficial effect when taken in too large quantities." - Lord Dunsany

See more famous quotes about Logic

 
Wikipedia: Logic (disambiguation)
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Look up logic in Wiktionary, the free dictionary.

Logic is the study of the principles and criteria of valid inference and demonstration.

Logic may also refer to:

Contents

In logic, philosophy, and mathematics

  • A branch of logic:
  • A branch of mathematics:
    • Symbolic logic, the area of mathematics that studies the purely formal properties of strings of symbols
    • Mathematical logic, a branch of mathematics that grew out of symbolic logic
  • A specific logical system or family of such systems in mathematical logic, such as:
  • A branch of philosophy:
    • Term logic, Traditional logic or philosophical logic beginning with Aristotle in Classical Greek philosophy
    • Classical logic, which embraces the principle of the excluded middle (P OR NOT P)

In computer science

  • Program logic, the use of mathematical logic for reasoning about computer programs

In computer technology

In software

  • Logic Studio, a music production suite by Apple Inc.
    • Logic Pro, a MIDI sequencer and Digital Audio Workstation application, part of Logic Studio
  • Dolby Pro Logic, also known as Pro Logic, a surround sound processing technology

 
Translations: Logic
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Dansk (Danish)
n. - logik

Nederlands (Dutch)
logica, denkleer, het logische, vanzelfsprekendheid, noodzakelijk verloop

Français (French)
n. - logique

Deutsch (German)
n. - Logik

Ελληνική (Greek)
n. - λογική (επιστήμη)

Italiano (Italian)
logica

Português (Portuguese)
n. - lógica (f)

Русский (Russian)
логика, логичность, здравый смысл, алгоритм

Español (Spanish)
n. - lógica

Svenska (Swedish)
n. - logik, följdriktighet, beviskraft

中文(简体)(Chinese (Simplified))
逻辑, 推理的方法, 论理学, 逻辑电路

中文(繁體)(Chinese (Traditional))
n. - 邏輯, 推理的方法, 論理學, 邏輯電路

한국어 (Korean)
n. - 논리학, 추리법, 이론, 조리

日本語 (Japanese)
n. - 論理学, 論理, 論法, もっともな考え, 道理

العربيه (Arabic)
‏(الاسم) علم المنطق, منطق العلم أو التاريخ أو الأحداث‏

עברית (Hebrew)
n. - ‮מדע החוקר את העקרונות השולטים בהסקה נכונה ואמינה, היגיון, שימוש נכון אן בלתי-נכון בטיעונים, לוגיקה, שרשרת מסקנות, שיקול-דעת, המסקנה ההכרחית מ(טענה, החלטה וכו'), פעולות הגיוניות‬


 
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Some good "logic" pages on the web:


American Sign Language
commtechlab.msu.edu
 

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Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved.  Read more
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Thesaurus. Roget's II: The New Thesaurus, Third Edition by the Editors of the American Heritage® Dictionary Copyright © 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.  Read more
Answers Corporation Antonyms. © 1999-2009 by Answers Corporation. All rights reserved.  Read more
Dental Dictionary. Mosby's Dental Dictionary. Copyright © 2004 by Elsevier, Inc. All rights reserved.  Read more
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History 1450-1789. Encyclopedia of the Early Modern World. Copyright © 2004 by The Gale Group, Inc. All rights reserved.  Read more
Veterinary Dictionary. Saunders Comprehensive Veterinary Dictionary 3rd Edition. Copyright © 2007 by D.C. Blood, V.P. Studdert and C.C. Gay, Elsevier. All rights reserved.  Read more
Electronics Dictionary. Copyright 2001 by Twysted Pair. All rights reserved.  Read more
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